Sample: There are 6157 complete cases on CAM variables at Wave 1.

CAM Descriptives

Frequencies and percentages on each variable

##              Item Category Frequency Percent Pcnt_of_nonMissing
## 1    aAcupuncture        0      6083    98.8               98.8
## 2    aAcupuncture        1        74     1.2                1.2
## 3    aBiofeedback        0      6109    99.2               99.2
## 4    aBiofeedback        1        48     0.8                0.8
## 5   aChiropractic        0      5418    88.0               88.0
## 6   aChiropractic        1       739    12.0               12.0
## 7     aEnergyHeal        0      6064    98.5               98.5
## 8     aEnergyHeal        1        93     1.5                1.5
## 9   aExerciseMove        0      5079    82.5               82.5
## 10  aExerciseMove        1      1078    17.5               17.5
## 11        aHerbal        0      5856    95.1               95.1
## 12        aHerbal        1       301     4.9                4.9
## 13      aVitamins        0      5875    95.4               95.4
## 14      aVitamins        1       282     4.6                4.6
## 15    aHomeopathy        0      6015    97.7               97.7
## 16    aHomeopathy        1       142     2.3                2.3
## 17      aHypnosis        0      6085    98.8               98.8
## 18      aHypnosis        1        72     1.2                1.2
## 19   aImageryTech        0      5973    97.0               97.0
## 20   aImageryTech        1       184     3.0                3.0
## 21       aMassage        0      5638    91.6               91.6
## 22       aMassage        1       519     8.4                8.4
## 23        aPrayer        0      4315    70.1               70.1
## 24        aPrayer        1      1842    29.9               29.9
## 25 aRelaxMeditate        0      5344    86.8               86.8
## 26 aRelaxMeditate        1       813    13.2               13.2
## 27   aSpecialDiet        0      5488    89.1               89.1
## 28   aSpecialDiet        1       669    10.9               10.9
## 29    aSpiritHeal        0      5961    96.8               96.8
## 30    aSpiritHeal        1       196     3.2                3.2

Visualization of frequencies

## Number of CAM treatments used in the past 12 months

## totalCams
##            0            1            2            3            4            5 
## 0.4866006172 0.2320935521 0.1279844080 0.0729251259 0.0328081858 0.0190027611 
##            6            7            8            9           10           11 
## 0.0120188403 0.0063342537 0.0040604190 0.0021114179 0.0019490011 0.0014617509 
##           13           15 
## 0.0004872503 0.0001624168
##  Category    f   rf rf(%)   cf  cf(%)
##         0 2996 0.49 48.66 2996  48.66
##         1 1429 0.23 23.21 4425  71.87
##         2  788 0.13 12.80 5213  84.67
##         3  449 0.07  7.29 5662  91.96
##         4  202 0.03  3.28 5864  95.24
##         5  117 0.02  1.90 5981  97.14
##         6   74 0.01  1.20 6055  98.34
##         7   39 0.01  0.63 6094  98.98
##         8   25 0.00  0.41 6119  99.38
##         9   13 0.00  0.21 6132  99.59
##        10   12 0.00  0.19 6144  99.79
##        11    9 0.00  0.15 6153  99.94
##        13    3 0.00  0.05 6156  99.98
##        15    1 0.00  0.02 6157 100.00

Analayses including all 15 CAMs

Correlation matrix

Create and plot the tetrachoric correlation matrix for all CAMs.

Check that items are not perfectly correlated with each other.

##                aA aB aC aEH aEM aHr aV aHm aHy aI aM aP aR aSD aSH
## aAcupuncture   1                                                  
## aBiofeedback   .  1                                               
## aChiropractic  .     1                                            
## aEnergyHeal    .  .  .  1                                         
## aExerciseMove     .     .   1                                     
## aHerbal        ,  .  .  ,   .   1                                 
## aVitamins      .        .   .   ,   1                             
## aHomeopathy    .  .  .  ,   .   ,   ,  1                          
## aHypnosis      .        .       .      .   1                      
## aImageryTech   .  .     ,   .   .   .  .   .   1                  
## aMassage       .  .  .  ,   .   .   .  .   .   .  1               
## aPrayer                 .   .   .   .  .       .     1            
## aRelaxMeditate .  ,     ,   .   .   .  .   .   +  .  .  1         
## aSpecialDiet   .        .   .   .   .  .       .  .  .  .  1      
## aSpiritHeal             .       .      .   .   .  .  ,  .  .   1  
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

Test for correlation adequacy

I will test for correlation adequacy using Bartlett’s Sphericity test. This test tests the hypothesis that correlations between variables are greater than would be expected by chance. The null hypothesis states that all off diagonal are 0. If the null hypothesis is rejected there is correlation adequacy.

## $chisq
## [1] 66329.56
## 
## $p.value
## [1] 0
## 
## $df
## [1] 105

I reject the null hypothesis. The CAM items are adequately correlated.

Test for sampling adequacy

I will test for sampling adequacy using the Kaiser-Meyer-Olkin (KMO) test.MSA refers to the overall measure of sampling adequacy. MSAi refer to the measure of sampling adequacy for each item. MSA is a measure of the proportion of variance among variables that might be common variance. The lower the proportion of variance that is common the more suited the data are for factor analysis.

MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = het.mat)
## Overall MSA =  0.76
## MSA for each item = 
##   aAcupuncture   aBiofeedback  aChiropractic    aEnergyHeal  aExerciseMove 
##           0.85           0.75           0.73           0.89           0.77 
##        aHerbal      aVitamins    aHomeopathy      aHypnosis   aImageryTech 
##           0.91           0.81           0.88           0.72           0.82 
##       aMassage        aPrayer aRelaxMeditate   aSpecialDiet    aSpiritHeal 
##           0.81           0.53           0.64           0.88           0.51

Items that may be a concern with regard to sampling adequacy: prayer or other spiritual practices, relaxation or meditation, and spiritual healing. Overall MSA indicates sampling adequacy.

Determining the number of factors

First, I will run a parallel analysis. From RDocumentation: “``Parallel” analyis is a technique that compares the scree of factors of the observed data with that of a random data matrix of the same size as the original."

Parallel analysis completed using maximum likelihood factoring method.

## Parallel analysis suggests that the number of factors =  6  and the number of components =  NA

I received many warning messages stating “A cell entry of 0 was replaced with correct = 0.5. Check your data!” This has to do with continuity when computing a tetrachoric correlation matrix. I added 1 to all values in the dataframe to check that the issue was not the 0/1 values. The results were the same.

From Statistics of DOOM notes: i. The dark line is set at one, which is part of the Kaiser criterion. This method is an older rule of thumb that is not well supported anymore. You would look at the number of eigenvalues that are greater than 1 (or .70 in new literature). This rule tends to overestimate the number of factors/components needed. ii. The red dotted line is the random data set used to test this analysis. Your data is randomly reordered to see how many factors are better than chance. iii. The blue line and triangles are your eigenvalues from the real dataset. iv. You want to look at where the blue and red lines cross.

The parallel analysis suggests 6 factors. This is where the lines cross. Looking at the scree plot, none of the drop offs appear to be very large. Seems like there are maybe 2 factors.

Note: Scree plots are a visual depiction of the eigenvalues. Look for the large drop off to figure out how many factors to use.

Kaiser Criterion

# older kaiser criterion, number of eigenvalues greater than 1 
sum(nofactors$fa.values > 1.0)
## [1] 1
# new kaiser criterion, number of eigenvalues greater than 0.7
sum(nofactors$fa.values > .7)
## [1] 2

New kaiser criterion rule (eigenvalues greater than 0.7) suggests 2 factors.

After readings Ayers and Kronenfeld (2010), I will test the old CAM domains posted by the National Center for Complementary and Alternative Medicine (NCCAM), now the National Center for Complementary and Integrative Medicine (NCCIM). Then I will test the domains found by Ayers and Kronenfeld (2010). Finally, I will test the NCCIM’s current CAM domains before performing exploratory factor analysis on the MIDUS data.

Fit Statistics: All models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully
## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully
## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully
## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully
##                Factors FactorMethod Rotation       BIC    TLI    CFI   RMSR
## 1mlvarimax           1           ml  varimax 22422.125 0.5927 0.6509 0.0918
## 1mlpromax            1           ml   promax 22422.125 0.5927 0.6509 0.0918
## 1mloblimin           1           ml  oblimin 22422.125 0.5927 0.6509 0.0918
## 1mlcluster           1           ml  cluster 22422.125 0.5927 0.6509 0.0918
## 1minresvarimax       1       minres  varimax 22461.997 0.5920 0.6503 0.0912
## 1minrespromax        1       minres   promax 22461.997 0.5920 0.6503 0.0912
## 1minresoblimin       1       minres  oblimin 22461.997 0.5920 0.6503 0.0912
## 1minrescluster       1       minres  cluster 22461.997 0.5920 0.6503 0.0912
## 1pavarimax           1           pa  varimax 22461.655 0.5920 0.6503 0.0912
## 1papromax            1           pa   promax 22461.655 0.5920 0.6503 0.0912
## 1paoblimin           1           pa  oblimin 22461.655 0.5920 0.6503 0.0912
## 1pacluster           1           pa  cluster 22461.655 0.5920 0.6503 0.0912
## 2mlvarimax           2           ml  varimax 17875.291 0.6148 0.7212 0.0748
## 2mlpromax            2           ml   promax 17875.291 0.6148 0.7212 0.0748
## 2mloblimin           2           ml  oblimin 17875.291 0.6148 0.7212 0.0748
## 2mlcluster           2           ml  cluster 17875.291 0.6148 0.7212 0.0748
## 2minresvarimax       2       minres  varimax 18414.251 0.6035 0.7131 0.0718
## 2minrespromax        2       minres   promax 18414.251 0.6035 0.7131 0.0718
## 2minresoblimin       2       minres  oblimin 18414.251 0.6035 0.7131 0.0718
## 2minrescluster       2       minres  cluster 18414.251 0.6035 0.7131 0.0718
## 2pavarimax           2           pa  varimax 18390.817 0.6040 0.7134 0.0718
## 2papromax            2           pa   promax 18390.817 0.6040 0.7134 0.0718
## 2paoblimin           2           pa  oblimin 18390.817 0.6040 0.7134 0.0718
## 2pacluster           2           pa  cluster 18390.817 0.6040 0.7134 0.0718
## 3mlvarimax           3           ml  varimax 11028.395 0.7101 0.8261 0.0632
## 3mlpromax            3           ml   promax 11028.395 0.7101 0.8261 0.0632
## 3mloblimin           3           ml  oblimin 11028.395 0.7101 0.8261 0.0632
## 3mlcluster           3           ml  cluster 11028.395 0.7101 0.8261 0.0632
## 3minresvarimax       3       minres  varimax 12896.066 0.6631 0.7979 0.0564
## 3minrespromax        3       minres   promax 12896.066 0.6631 0.7979 0.0564
## 3minresoblimin       3       minres  oblimin 12896.066 0.6631 0.7979 0.0564
## 3minrescluster       3       minres  cluster 12896.066 0.6631 0.7979 0.0564
## 3pavarimax           3           pa  varimax 12919.180 0.6625 0.7976 0.0564
## 3papromax            3           pa   promax 12919.180 0.6625 0.7976 0.0564
## 3paoblimin           3           pa  oblimin 12919.180 0.6625 0.7976 0.0564
## 3pacluster           3           pa  cluster 12919.180 0.6625 0.7976 0.0564
## 4mlvarimax           4           ml  varimax  7272.309 0.7616 0.8842 0.0556
## 4mlpromax            4           ml   promax  7272.309 0.7616 0.8842 0.0556
## 4mloblimin           4           ml  oblimin  7272.309 0.7616 0.8842 0.0556
## 4mlcluster           4           ml  cluster  7272.309 0.7616 0.8842 0.0556
## 4minresvarimax       4       minres  varimax 10755.623 0.6532 0.8316 0.0434
## 4minrespromax        4       minres   promax 10755.623 0.6532 0.8316 0.0434
## 4minresoblimin       4       minres  oblimin 10755.623 0.6532 0.8316 0.0434
## 4minrescluster       4       minres  cluster 10755.623 0.6532 0.8316 0.0434
## 4pavarimax           4           pa  varimax 10935.463 0.6476 0.8289 0.0440
## 4papromax            4           pa   promax 10935.463 0.6476 0.8289 0.0440
## 4paoblimin           4           pa  oblimin 10935.463 0.6476 0.8289 0.0440
## 4pacluster           4           pa  cluster 10935.463 0.6476 0.8289 0.0440
## 5mlvarimax           5           ml  varimax  4600.918 0.8053 0.9259 0.0419
## 5mlpromax            5           ml   promax  4600.918 0.8053 0.9259 0.0419
## 5mloblimin           5           ml  oblimin  4600.918 0.8053 0.9259 0.0419
## 5mlcluster           5           ml  cluster  4600.918 0.8053 0.9259 0.0419
## 5minresvarimax       5       minres  varimax  7198.159 0.7023 0.8866 0.0286
## 5minrespromax        5       minres   promax  7198.159 0.7023 0.8866 0.0286
## 5minresoblimin       5       minres  oblimin  7198.159 0.7023 0.8866 0.0286
## 5minrescluster       5       minres  cluster  7198.159 0.7023 0.8866 0.0286
## 5pavarimax           5           pa  varimax  7912.753 0.6739 0.8759 0.0309
## 5papromax            5           pa   promax  7912.753 0.6739 0.8759 0.0309
## 5paoblimin           5           pa  oblimin  7912.753 0.6739 0.8759 0.0309
## 5pacluster           5           pa  cluster  7912.753 0.6739 0.8759 0.0309
## 6mlvarimax           6           ml  varimax  3151.229 0.8211 0.9489 0.0290
## 6mlpromax            6           ml   promax  3151.229 0.8211 0.9489 0.0290
## 6mloblimin           6           ml  oblimin  3151.229 0.8211 0.9489 0.0290
## 6mlcluster           6           ml  cluster  3151.229 0.8211 0.9489 0.0290
## 6minresvarimax       6       minres  varimax  6429.609 0.6477 0.8994 0.0224
## 6minrespromax        6       minres   promax  6429.609 0.6477 0.8994 0.0224
## 6minresoblimin       6       minres  oblimin  6429.609 0.6477 0.8994 0.0224
## 6minrescluster       6       minres  cluster  6429.609 0.6477 0.8994 0.0224
## 6pavarimax           6           pa  varimax  5001.737 0.7232 0.9210 0.0214
## 6papromax            6           pa   promax  5001.737 0.7232 0.9210 0.0214
## 6paoblimin           6           pa  oblimin  5001.737 0.7232 0.9210 0.0214
## 6pacluster           6           pa  cluster  5001.737 0.7232 0.9210 0.0214
##                 RMSEA
## 1mlvarimax     0.2043
## 1mlpromax      0.2043
## 1mloblimin     0.2043
## 1mlcluster     0.2043
## 1minresvarimax 0.2044
## 1minrespromax  0.2044
## 1minresoblimin 0.2044
## 1minrescluster 0.2044
## 1pavarimax     0.2044
## 1papromax      0.2044
## 1paoblimin     0.2044
## 1pacluster     0.2044
## 2mlvarimax     0.1986
## 2mlpromax      0.1986
## 2mloblimin     0.1986
## 2mlcluster     0.1986
## 2minresvarimax 0.2015
## 2minrespromax  0.2015
## 2minresoblimin 0.2015
## 2minrescluster 0.2015
## 2pavarimax     0.2014
## 2papromax      0.2014
## 2paoblimin     0.2014
## 2pacluster     0.2014
## 3mlvarimax     0.1723
## 3mlpromax      0.1723
## 3mloblimin     0.1723
## 3mlcluster     0.1723
## 3minresvarimax 0.1857
## 3minrespromax  0.1857
## 3minresoblimin 0.1857
## 3minrescluster 0.1857
## 3pavarimax     0.1859
## 3papromax      0.1859
## 3paoblimin     0.1859
## 3pacluster     0.1859
## 4mlvarimax     0.1563
## 4mlpromax      0.1563
## 4mloblimin     0.1563
## 4mlcluster     0.1563
## 4minresvarimax 0.1884
## 4minrespromax  0.1884
## 4minresoblimin 0.1884
## 4minrescluster 0.1884
## 4pavarimax     0.1899
## 4papromax      0.1899
## 4paoblimin     0.1899
## 4pacluster     0.1899
## 5mlvarimax     0.1412
## 5mlpromax      0.1412
## 5mloblimin     0.1412
## 5mlcluster     0.1412
## 5minresvarimax 0.1746
## 5minrespromax  0.1746
## 5minresoblimin 0.1746
## 5minrescluster 0.1746
## 5pavarimax     0.1827
## 5papromax      0.1827
## 5paoblimin     0.1827
## 5pacluster     0.1827
## 6mlvarimax     0.1353
## 6mlpromax      0.1353
## 6mloblimin     0.1353
## 6mlcluster     0.1353
## 6minresvarimax 0.1899
## 6minrespromax  0.1899
## 6minresoblimin 0.1899
## 6minrescluster 0.1899
## 6pavarimax     0.1683
## 6papromax      0.1683
## 6paoblimin     0.1683
## 6pacluster     0.1683

Factor loadings: All Models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## maximum iteration exceeded
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## [[1]]
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Exclude prayer and spiritual healing

Tetrachoric correlations (excluding prayer and spiritual healing)

Test for correlation adequacy

Bartlett’s test for sphericity.

## $chisq
## [1] 51305.93
## 
## $p.value
## [1] 0
## 
## $df
## [1] 78

Items are adequately correlated.

Test for sampling adequacy

MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.

## [1] 0.886576
##  aChiropractic      aHypnosis   aBiofeedback  aExerciseMove aRelaxMeditate 
##      0.8014794      0.8513482      0.8561802      0.8593921      0.8623881 
##       aMassage   aImageryTech   aSpecialDiet        aHerbal   aAcupuncture 
##      0.8803881      0.8905944      0.8923741      0.8965394      0.8988504 
##    aHomeopathy      aVitamins    aEnergyHeal 
##      0.9057442      0.9083067      0.9361243

Determining number of factors

Parallel Analysis

## Parallel analysis suggests that the number of factors =  5  and the number of components =  NA

The parallel analysis suggests 5 factors. There is a drop off on the scree plot after 4.

Kaiser Criterion

Older kaiser criterion suggests number of factors is equal to the number of eigenvalues greater than 1. The new kaiser criterion suggests numbers of factors is equal to the number of eigenvalues greater than 0.7

##  [1] 6.5668 1.1133 1.0560 1.0129 0.7291 0.5862 0.4995 0.3394 0.2891 0.2793
## [11] 0.2126 0.1776 0.1380

Suggests 4 or 5 factors.

Reliability among ACAMs excluding prayer and spiritual healing

##  raw_alpha std.alpha  G6(smc) average_r      S/N         ase      mean       sd
##  0.6826334  0.712388 0.713637 0.1600388 2.476906 0.005549916 0.0626429 0.107813
##   median_r
##  0.1581703

Removing prayer and spiritual healing does not improve the reliability at all. Raw alpha is almost exactly the same, 0.68. Lowers reliability slightly (from 0.695).

##Fit Statistics: All models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
##                Factors FactorMethod Rotation      BIC    TLI    CFI   RMSR
## 2mlvarimax           2           ml  varimax 6071.832 0.8138 0.8735 0.0648
## 2mlpromax            2           ml   promax 6071.832 0.8138 0.8735 0.0648
## 2mloblimin           2           ml  oblimin 6071.832 0.8138 0.8735 0.0648
## 2mlcluster           2           ml  cluster 6071.832 0.8138 0.8735 0.0648
## 2minresvarimax       2       minres  varimax 6259.199 0.8084 0.8698 0.0628
## 2minrespromax        2       minres   promax 6259.199 0.8084 0.8698 0.0628
## 2minresoblimin       2       minres  oblimin 6259.199 0.8084 0.8698 0.0628
## 2minrescluster       2       minres  cluster 6259.199 0.8084 0.8698 0.0628
## 3mlvarimax           3           ml  varimax 4139.058 0.8381 0.9129 0.0510
## 3mlpromax            3           ml   promax 4139.058 0.8381 0.9129 0.0510
## 3mloblimin           3           ml  oblimin 4139.058 0.8381 0.9129 0.0510
## 3mlcluster           3           ml  cluster 4139.058 0.8381 0.9129 0.0510
## 3minresvarimax       3       minres  varimax 4206.168 0.8357 0.9116 0.0479
## 3minrespromax        3       minres   promax 4206.168 0.8357 0.9116 0.0479
## 3minresoblimin       3       minres  oblimin 4206.168 0.8357 0.9116 0.0479
## 3minrescluster       3       minres  cluster 4206.168 0.8357 0.9116 0.0479
## 4mlvarimax           4           ml  varimax 2266.928 0.8803 0.9509 0.0300
## 4mlpromax            4           ml   promax 2266.928 0.8803 0.9509 0.0300
## 4mloblimin           4           ml  oblimin 2266.928 0.8803 0.9509 0.0300
## 4mlcluster           4           ml  cluster 2266.928 0.8803 0.9509 0.0300
## 4minresvarimax       4       minres  varimax 2436.929 0.8722 0.9476 0.0283
## 4minrespromax        4       minres   promax 2436.929 0.8722 0.9476 0.0283
## 4minresoblimin       4       minres  oblimin 2436.929 0.8722 0.9476 0.0283
## 4minrescluster       4       minres  cluster 2436.929 0.8722 0.9476 0.0283
## 5mlvarimax           5           ml  varimax 1167.187 0.9109 0.9737 0.0201
## 5mlpromax            5           ml   promax 1167.187 0.9109 0.9737 0.0201
## 5mloblimin           5           ml  oblimin 1167.187 0.9109 0.9737 0.0201
## 5mlcluster           5           ml  cluster 1167.187 0.9109 0.9737 0.0201
## 5minresvarimax       5       minres  varimax 1352.568 0.8986 0.9701 0.0183
## 5minrespromax        5       minres   promax 1352.568 0.8986 0.9701 0.0183
## 5minresoblimin       5       minres  oblimin 1352.568 0.8986 0.9701 0.0183
## 5minrescluster       5       minres  cluster 1352.568 0.8986 0.9701 0.0183
##                 RMSEA
## 2mlvarimax     0.1409
## 2mlpromax      0.1409
## 2mloblimin     0.1409
## 2mlcluster     0.1409
## 2minresvarimax 0.1430
## 2minrespromax  0.1430
## 2minresoblimin 0.1430
## 2minrescluster 0.1430
## 3mlvarimax     0.1314
## 3mlpromax      0.1314
## 3mloblimin     0.1314
## 3mlcluster     0.1314
## 3minresvarimax 0.1324
## 3minrespromax  0.1324
## 3minresoblimin 0.1324
## 3minrescluster 0.1324
## 4mlvarimax     0.1130
## 4mlpromax      0.1130
## 4mloblimin     0.1130
## 4mlcluster     0.1130
## 4minresvarimax 0.1167
## 4minrespromax  0.1167
## 4minresoblimin 0.1167
## 4minrescluster 0.1167
## 5mlvarimax     0.0975
## 5mlpromax      0.0975
## 5mloblimin     0.0975
## 5mlcluster     0.0975
## 5minresvarimax 0.1040
## 5minrespromax  0.1040
## 5minresoblimin 0.1040
## 5minrescluster 0.1040

Factor loadings: 3 through 5 factor models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## [[1]]
## [[1]][[1]]
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## NULL

Exclude prayer, spiritual healing, and energy healing

Tetrachoric correlation matrix

## Bartlett’s Test of Spherecity I will test for correlation adequacy using Bartlett’s Sphericity test. This test tests the hypothesis that correlations between variables are greater than would be expected by chance. The null hypothesis states that all off diagonal are 0. If the null hypothesis is rejected there is correlation adequacy.

## $chisq
## [1] 42574.65
## 
## $p.value
## [1] 0
## 
## $df
## [1] 66

KMO Test for sampling adequacy

MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.

## [1] 0.8625341
##  aChiropractic aRelaxMeditate  aExerciseMove   aBiofeedback      aHypnosis 
##      0.7969845      0.8321353      0.8337881      0.8487751      0.8574957 
##       aMassage   aImageryTech        aHerbal   aAcupuncture   aSpecialDiet 
##      0.8660164      0.8707506      0.8708735      0.8737196      0.8834541 
##    aHomeopathy      aVitamins 
##      0.8912350      0.8944847

Great.

Parallel Analysis

First, I will run a parallel analysis. From RDocumentation: “``Parallel” analyis is a technique that compares the scree of factors of the observed data with that of a random data matrix of the same size as the original."

## Parallel analysis suggests that the number of factors =  5  and the number of components =  NA

The parallel analysis suggests 5 factors. This is where the lines cross. Looking at the scree plot, there is a drop at 4 factors.

Kaiser Criterion

Older kaiser criterion suggests number of factors is equal to the number of eigenvalues greater than 1. The new kaiser criterion suggests numbers of factors is equal to the number of eigenvalues greater than 0.7

##  [1] 5.8080 1.1060 1.0447 1.0128 0.7267 0.5841 0.4935 0.3361 0.2866 0.2784
## [11] 0.1776 0.1455

Indicates 4 or 5 factors.

##Fit Statistics: All models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
##                Factors FactorMethod Rotation      BIC    TLI    CFI   RMSR
## 2mlvarimax           2           ml  varimax 5469.563 0.7905 0.8635 0.0696
## 2mlpromax            2           ml   promax 5469.563 0.7905 0.8635 0.0696
## 2mloblimin           2           ml  oblimin 5469.563 0.7905 0.8635 0.0696
## 2mlcluster           2           ml  cluster 5469.563 0.7905 0.8635 0.0696
## 2minresvarimax       2       minres  varimax 5678.340 0.7829 0.8586 0.0669
## 2minrespromax        2       minres   promax 5678.340 0.7829 0.8586 0.0669
## 2minresoblimin       2       minres  oblimin 5678.340 0.7829 0.8586 0.0669
## 2minrescluster       2       minres  cluster 5678.340 0.7829 0.8586 0.0669
## 2pavarimax           2           pa  varimax 5669.949 0.7832 0.8588 0.0669
## 2papromax            2           pa   promax 5669.949 0.7832 0.8588 0.0669
## 2paoblimin           2           pa  oblimin 5669.949 0.7832 0.8588 0.0669
## 2pacluster           2           pa  cluster 5669.949 0.7832 0.8588 0.0669
## 3mlvarimax           3           ml  varimax 3395.890 0.8282 0.9141 0.0536
## 3mlpromax            3           ml   promax 3395.890 0.8282 0.9141 0.0536
## 3mloblimin           3           ml  oblimin 3395.890 0.8282 0.9141 0.0536
## 3mlcluster           3           ml  cluster 3395.890 0.8282 0.9141 0.0536
## 3minresvarimax       3       minres  varimax 3690.383 0.8143 0.9072 0.0507
## 3minrespromax        3       minres   promax 3690.383 0.8143 0.9072 0.0507
## 3minresoblimin       3       minres  oblimin 3690.383 0.8143 0.9072 0.0507
## 3minrescluster       3       minres  cluster 3690.383 0.8143 0.9072 0.0507
## 3pavarimax           3           pa  varimax 3674.177 0.8151 0.9076 0.0507
## 3papromax            3           pa   promax 3674.177 0.8151 0.9076 0.0507
## 3paoblimin           3           pa  oblimin 3674.177 0.8151 0.9076 0.0507
## 3pacluster           3           pa  cluster 3674.177 0.8151 0.9076 0.0507
## 4mlvarimax           4           ml  varimax 1788.721 0.8722 0.9536 0.0317
## 4mlpromax            4           ml   promax 1788.721 0.8722 0.9536 0.0317
## 4mloblimin           4           ml  oblimin 1788.721 0.8722 0.9536 0.0317
## 4mlcluster           4           ml  cluster 1788.721 0.8722 0.9536 0.0317
## 4minresvarimax       4       minres  varimax 2012.150 0.8578 0.9483 0.0287
## 4minrespromax        4       minres   promax 2012.150 0.8578 0.9483 0.0287
## 4minresoblimin       4       minres  oblimin 2012.150 0.8578 0.9483 0.0287
## 4minrescluster       4       minres  cluster 2012.150 0.8578 0.9483 0.0287
## 4pavarimax           4           pa  varimax 2008.638 0.8580 0.9484 0.0287
## 4papromax            4           pa   promax 2008.638 0.8580 0.9484 0.0287
## 4paoblimin           4           pa  oblimin 2008.638 0.8580 0.9484 0.0287
## 4pacluster           4           pa  cluster 2008.638 0.8580 0.9484 0.0287
## 5mlvarimax           5           ml  varimax  912.527 0.8994 0.9756 0.0205
## 5mlpromax            5           ml   promax  912.527 0.8994 0.9756 0.0205
## 5mloblimin           5           ml  oblimin  912.527 0.8994 0.9756 0.0205
## 5mlcluster           5           ml  cluster  912.527 0.8994 0.9756 0.0205
## 5minresvarimax       5       minres  varimax 1060.848 0.8850 0.9721 0.0184
## 5minrespromax        5       minres   promax 1060.848 0.8850 0.9721 0.0184
## 5minresoblimin       5       minres  oblimin 1060.848 0.8850 0.9721 0.0184
## 5minrescluster       5       minres  cluster 1060.848 0.8850 0.9721 0.0184
## 5pavarimax           5           pa  varimax 1082.307 0.8829 0.9716 0.0184
## 5papromax            5           pa   promax 1082.307 0.8829 0.9716 0.0184
## 5paoblimin           5           pa  oblimin 1082.307 0.8829 0.9716 0.0184
## 5pacluster           5           pa  cluster 1082.307 0.8829 0.9716 0.0184
##                 RMSEA
## 2mlvarimax     0.1480
## 2mlpromax      0.1480
## 2mloblimin     0.1480
## 2mlcluster     0.1480
## 2minresvarimax 0.1507
## 2minrespromax  0.1507
## 2minresoblimin 0.1507
## 2minrescluster 0.1507
## 2pavarimax     0.1506
## 2papromax      0.1506
## 2paoblimin     0.1506
## 2pacluster     0.1506
## 3mlvarimax     0.1340
## 3mlpromax      0.1340
## 3mloblimin     0.1340
## 3mlcluster     0.1340
## 3minresvarimax 0.1393
## 3minrespromax  0.1393
## 3minresoblimin 0.1393
## 3minrescluster 0.1393
## 3pavarimax     0.1391
## 3papromax      0.1391
## 3paoblimin     0.1391
## 3pacluster     0.1391
## 4mlvarimax     0.1156
## 4mlpromax      0.1156
## 4mloblimin     0.1156
## 4mlcluster     0.1156
## 4minresvarimax 0.1219
## 4minrespromax  0.1219
## 4minresoblimin 0.1219
## 4minrescluster 0.1219
## 4pavarimax     0.1219
## 4papromax      0.1219
## 4paoblimin     0.1219
## 4pacluster     0.1219
## 5mlvarimax     0.1026
## 5mlpromax      0.1026
## 5mloblimin     0.1026
## 5mlcluster     0.1026
## 5minresvarimax 0.1097
## 5minrespromax  0.1097
## 5minresoblimin 0.1097
## 5minrescluster 0.1097
## 5pavarimax     0.1106
## 5papromax      0.1106
## 5paoblimin     0.1106
## 5pacluster     0.1106

Factor loadings: Three through 5 factor models

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully

## [[1]]
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Excluding prayer, spiritual healing, biofeedback, and hypnosis.

Tetrachoric correlations

## Bartlett’s Test of Spherecity I will test for correlation adequacy using Bartlett’s Sphericity test. This test tests the hypothesis that correlations between variables are greater than would be expected by chance. The null hypothesis states that all off diagonal are 0. If the null hypothesis is rejected there is correlation adequacy.

## $chisq
## [1] 8540.367
## 
## $p.value
## [1] 0
## 
## $df
## [1] 55

KMO Test for sampling adequacy

MSA cutoffs: >.9 marvelous, .8s meritorious, .7s middling, .6s mediocre, .5s miserable, less than .5 is unacceptable.

## [1] 0.8119214
##  aChiropractic   aImageryTech       aMassage aRelaxMeditate  aExerciseMove 
##      0.7597641      0.7805104      0.7990479      0.8100055      0.8103004 
##        aHerbal    aHomeopathy   aSpecialDiet      aVitamins    aEnergyHeal 
##      0.8123552      0.8125993      0.8307527      0.8385329      0.8390753 
##   aAcupuncture 
##      0.8410255

Parallel Analysis

## Parallel analysis suggests that the number of factors =  4  and the number of components =  NA

Suggests 4 factors.

Kaiser Criterion

##  [1] 2.9624 1.1136 1.0788 1.0116 0.8698 0.7710 0.7337 0.6914 0.6340 0.5710
## [11] 0.5627

Suggests 4 factors. ## Fit Statistics: All models

##                Factors FactorMethod Rotation      BIC    TLI    CFI   RMSR
## 3mlvarimax           3           ml  varimax 108.0315 0.9219 0.9645 0.0253
## 3mlpromax            3           ml   promax 108.0315 0.9219 0.9645 0.0253
## 3mloblimin           3           ml  oblimin 108.0315 0.9219 0.9645 0.0253
## 3mlcluster           3           ml  cluster 108.0315 0.9219 0.9645 0.0253
## 3minresvarimax       3       minres  varimax 112.3103 0.9208 0.9640 0.0252
## 3minrespromax        3       minres   promax 112.3103 0.9208 0.9640 0.0252
## 3minresoblimin       3       minres  oblimin 112.3103 0.9208 0.9640 0.0252
## 3minrescluster       3       minres  cluster 112.3103 0.9208 0.9640 0.0252
## 4mlvarimax           4           ml  varimax -89.2553 0.9840 0.9950 0.0100
## 4mlpromax            4           ml   promax -89.2553 0.9840 0.9950 0.0100
## 4mloblimin           4           ml  oblimin -89.2553 0.9840 0.9950 0.0100
## 4mlcluster           4           ml  cluster -89.2553 0.9840 0.9950 0.0100
## 4minresvarimax       4       minres  varimax -88.0262 0.9835 0.9949 0.0098
## 4minrespromax        4       minres   promax -88.0262 0.9835 0.9949 0.0098
## 4minresoblimin       4       minres  oblimin -88.0262 0.9835 0.9949 0.0098
## 4minrescluster       4       minres  cluster -88.0262 0.9835 0.9949 0.0098
## 5mlvarimax           5           ml  varimax -60.6944 0.9893 0.9980 0.0063
## 5mlpromax            5           ml   promax -60.6944 0.9893 0.9980 0.0063
## 5mloblimin           5           ml  oblimin -60.6944 0.9893 0.9980 0.0063
## 5mlcluster           5           ml  cluster -60.6944 0.9893 0.9980 0.0063
## 5minresvarimax       5       minres  varimax -60.8845 0.9894 0.9981 0.0060
## 5minrespromax        5       minres   promax -60.8845 0.9894 0.9981 0.0060
## 5minresoblimin       5       minres  oblimin -60.8845 0.9894 0.9981 0.0060
## 5minrescluster       5       minres  cluster -60.8845 0.9894 0.9981 0.0060
##                 RMSEA
## 3mlvarimax     0.0442
## 3mlpromax      0.0442
## 3mloblimin     0.0442
## 3mlcluster     0.0442
## 3minresvarimax 0.0445
## 3minrespromax  0.0445
## 3minresoblimin 0.0445
## 3minrescluster 0.0445
## 4mlvarimax     0.0200
## 4mlpromax      0.0200
## 4mloblimin     0.0200
## 4mlcluster     0.0200
## 4minresvarimax 0.0203
## 4minrespromax  0.0203
## 4minresoblimin 0.0203
## 4minrescluster 0.0203
## 5mlvarimax     0.0164
## 5mlpromax      0.0164
## 5mloblimin     0.0164
## 5mlcluster     0.0164
## 5minresvarimax 0.0163
## 5minrespromax  0.0163
## 5minresoblimin 0.0163
## 5minrescluster 0.0163

Factor loadings: 3 through 5 factor models

## [[1]]
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